A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemic...A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemical calculation.The calculated results are in good agreement with that obtained in the experiments.Three Cl atoms are on the same side of Ln in LnCl_3·15-C-5 and the crown ring on the other side.forming a complex molecule with coordination number 8.LnCl_3·15-C-5 is easily hygroscopic in air because of its unsaturated coordination,which differs sharply from the stable Ln(NO_3)_3·15-C-5 com- plex of coordination number 11.The HOMO and neighboring occupied MOs are composed of Cl 3p and O2p, and the LUMO and neighboring unoccupied MOs are composed of Ln orbitals.The level structure easily pro- duces Ln3d satellite in XPS caused by L→Ln charge transfer transition.Due to the coordination,the absolute values of the charge are decreased at Ln and O atoms,but increased at Cl atoms,which is in agreement with XPS results.展开更多
For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some char...Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.展开更多
文摘A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemical calculation.The calculated results are in good agreement with that obtained in the experiments.Three Cl atoms are on the same side of Ln in LnCl_3·15-C-5 and the crown ring on the other side.forming a complex molecule with coordination number 8.LnCl_3·15-C-5 is easily hygroscopic in air because of its unsaturated coordination,which differs sharply from the stable Ln(NO_3)_3·15-C-5 com- plex of coordination number 11.The HOMO and neighboring occupied MOs are composed of Cl 3p and O2p, and the LUMO and neighboring unoccupied MOs are composed of Ln orbitals.The level structure easily pro- duces Ln3d satellite in XPS caused by L→Ln charge transfer transition.Due to the coordination,the absolute values of the charge are decreased at Ln and O atoms,but increased at Cl atoms,which is in agreement with XPS results.
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
基金supported by NSFC(12071484)Hunan Provincial Natural Science Foundation(2020JJ4675)Foundation of Guangdong University of Science and Technology.
文摘Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.
